Free convection boundary layer over a nonisothermal vertical flat plate

Abstract

Numerical solutions are presented for the free convection boundary layer problems on a vertical flat plate with prescribed temperature or heat flux distributions, namely the sinusoidal wall temperature and the exponential heat flux variations. The numerical computation is carried out using a very efficient implicit finite difference scheme known as the Keller-box method. Illustrative computational examples are carried out and the present results are compared with previously available theoretical results obtained using other methods of solution, and they are found to be in good agreement. Comparisons of nondimensional temperature gradient for sinusoidal wall temperature variation and of nondimensional wall temperature with exponential variation in wall heat flux are made between the present and previous results. New results for the variation of the surface shear stress with various Prandtl numbers are also presented. In addition, for the case of sinusoidal wall temperature variation, representative velocity and temperature profiles are presented for Prandtl numbers 0.7, 1, 10 and 100, while for the case of exponential heat flux distribution, the velocity and temperature profiles for various transformed streamwise coordinate î = 0, 1, 10 and 100 are illustrated.